Question
What is the least common multiple of four and three
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Answered by
GPT-4o mini
To find the least common multiple (LCM) of 4 and 3, we can list the multiples of each number:
- The multiples of 4 are: 4, 8, 12, 16, 20, ...
- The multiples of 3 are: 3, 6, 9, 12, 15, ...
The smallest multiple that appears in both lists is 12. Therefore, the least common multiple of 4 and 3 is **12**.
Alternatively, you can also calculate the LCM using the formula:
\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}
\]
Here, the greatest common divisor (GCD) of 4 and 3 is 1, since they have no common factors other than 1.
\[
\text{LCM}(4, 3) = \frac{|4 \times 3|}{1} = \frac{12}{1} = 12
\]
So, the LCM of 4 and 3 is indeed **12**.
- The multiples of 4 are: 4, 8, 12, 16, 20, ...
- The multiples of 3 are: 3, 6, 9, 12, 15, ...
The smallest multiple that appears in both lists is 12. Therefore, the least common multiple of 4 and 3 is **12**.
Alternatively, you can also calculate the LCM using the formula:
\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}
\]
Here, the greatest common divisor (GCD) of 4 and 3 is 1, since they have no common factors other than 1.
\[
\text{LCM}(4, 3) = \frac{|4 \times 3|}{1} = \frac{12}{1} = 12
\]
So, the LCM of 4 and 3 is indeed **12**.
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